Input interpretation complete the square | 28 + 10 x + x^2 Result (x + 5)^2 + 3 Geometric figure parabola Polynomial discriminant Delta = -12 Derivative d/dx((x + 5)^2 + 3) = 2 (x + 5) Indefinite integral integral (3 + (5 + x)^2) dx = x^3/3 + 5 …

Input Arithmetic series Arithmetic series sum_(k=1)^n(a_1 + (k – 1) d) = n a_1 + 1/2 n ((n – 1) d)

Input interpretation arithmetic progression Alternate name arithmetic sequence Definition An arithmetic progression, also known as an arithmetic sequence, is a sequence of n numbers {a_0 + kd}_(k = 0)^(n – 1) such that the differences between successive terms is a constant d. An arithmetic progression can be generated in the …

Input interpretation Y-intercepts | Y = X Result Y = 0 Y-intercept point (X, Y) = (0, 0)

Input interpretation plane curve | Cartesian equation y = 1 + 3 x | x-intercept Result -1/3~~-0.333333 Geometric figure line Properties of line x-intercept | -1/3~~-0.333333 y-intercept | 1 slope | 3

Input abs(x) Alternate form assuming x>0 x Alternate form assuming x is real sqrt(x^2) Root x = 0 Derivative d/dx(abs(x)) = x/abs(x) (assuming a function from reals to reals) Indefinite integral assuming all variables are real integral abs(x) dx = 1/2 x^2 sgn(x) + constant Global minimum min{abs(x)} = 0 …